With the help of [1]} and [2]}, we can express the \(exp(\cdot )\)  function in terms of the Mellin-Barnes integral form as
\(&\exp \!\left( { - \frac{{x - {\sigma ^2}}}{{{P_{Ik}}{\eta _k}}}} \right) = G_{0,1}^{1,0}\left( {\left. {\frac{{x - {\sigma ^2}}}{{{P_{Ik}}{\eta _k}}}} \right|0} \right)\\& = \frac{1}{{2\pi i}}\int _{{{\cal L}_1}} {\Gamma \!\left( { - {s_1}} \right)} {\left( {\frac{{x - {\sigma ^2}}}{{{P_{Ik}}{\eta _k}}}} \right)^{{s_1}}}{\rm {d}}{s_1}.\) 
